derivative of (40/(x^5))

解答

\frac{d}{d x} (\frac{40}{x ^{5}})

- \frac{200}{x ^{6}}

求解步骤

\frac{d}{d x} (\frac{40}{x ^{5}})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 40 \frac{d}{d x} (\frac{1}{x ^{5}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 40 \frac{d}{d x} (x^{- 5})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 40 (- 5 x^{- 5 - 1})

化简

40 (- 5 x^{- 5 - 1}) : - \frac{200}{x ^{6}}

= - \frac{200}{x ^{6}}

\frac{\partial}{\partial x} (- y e^{x})

\frac{d}{d z} (ln (\frac{d ^{2} - z ^{2}}{d ^{2} + z ^{2}}))

d er i v a t i v e \frac{x}{9 - x ^{2}}

x \to - 3 lim (- 1.2 x - 4.6)

\frac{d}{d x} (\frac{x ^{2}}{1 + 6 x})